Abstract
The theory of nonstationary thermophoresis of a solid spherical particle in a viscous gaseous medium is presented. The theory is constructed on the solutions of fluid-dynamics and thermal problems, each of which is split into stationary and strictly nonstationary parts. The solution of the stationary parts of the problems gives the final formula for determining the stationary component of the thermophoretic velocity of this particle. To determine the nonstationary component of the thermophoretic velocity of the particle, the corresponding formula in the space of Laplace transforms is derived. The limiting value theorems from operational calculus are used for obtaining the dependence of the nonstationary component of the thermophoretic velocity of the spherical particle on the strictly nonstationary temperature gradient for large and small values of time. The factors determining the thermophoretic velocity of the particle under investigation are determined.
Similar content being viewed by others
References
N. A. Fuks, Mechanics of Aerosols (Izd. Akad. Nauk SSSR, Moscow, 1955; US Department of Commerce, Washington, 1958).
Yu. I. Yalamov and V. S. Galoyan, Dynamics of Drops in Inhomogeneous Viscous Media (Luĭs, Yerevan, 1985) [in Russian].
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Fizmatlit, Moscow, 2001; Pergamon, New York, 1987).
N. A. Slezkin, Dynamics of Viscous Incompressible Fluid (Gostekhizdat, Moscow, 1955) [in Russian].
J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Prentice-Hall, Englewood Cliffs, 1965; Mir, Moscow, 1976).
E. Kamke, Gewohnliche Differentialgleichungen (Acad. Verlag, Leipzig, 1959; Nauka, Moscow, 1976) [translated from German].
G. Doetsch, Guide to the Applications of the Laplace and Z-Transforms, 2nd ed. (Van Nostrand-Reinhold, London, 1971; Nauka, Moscow, 1971).
B. G. Korenev, Introduction to the Theory of Bessel Functions (Nauka, Moscow, 1971) [in Russian].
A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics (MGU, Moscow, 2004; Dover, New York, 1990).
Author information
Authors and Affiliations
Additional information
Original Russian Text © M.K. Kuzmin, Yu.I. Yalamov, 2007, published in Zhurnal Tekhnicheskoĭ Fiziki, 2007, Vol. 77, No. 6, pp. 1–7.